Julia Gillard has rejected claims that she is playing politics with the issue of Tony Abbott's trip to Afghanistan.

Mr Abbott found himself on the backfoot yesterday when he said he had declined the chance to visit Afghanistan with Ms Gillard at the weekend because he did not want to be jet-lagged during his trip to the Conservative Party conference in England.

Mr Abbott has since admitted he chose his words poorly, and the Opposition's treasury spokesman, Joe Hockey, says Ms Gillard knew all along that the Opposition Leader had already locked in another date to visit Australian troops on the front line.

But Ms Gillard, who initially quipped that she would leave Mr Abbott's "sleeping patterns" up to him, says he only has himself to blame for the controversy.

"The matter has become the subject of public controversy because of some statements Mr Abbott made and at no time have I sought to add to that debate," she said at the end of the two-day Asia-Europe Meeting (ASEM) in Brussels.

Ms Gillard says it is wrong to suggest that she knew Mr Abbott was already planning a trip of his own.

"[The] suggestion that he had a fixed date to go when I issued the invitation to him is not correct," she said. "It's simply not correct."

Mr Abbott says he intends to travel to Afghanistan shortly but will do so at a time of his choosing.

He says Australia's commitment to Afghanistan should not be politicised.

"There's been bipartisan support for [the war effort]," he said.

"I think our troops in Afghanistan deserve bipartisan support.

"I certainly don't call into question the Prime Minister's commitment to our troops in Afghanistan, and I think she shouldn't question mine."

Ms Gillard has now flown out of Brussels after signing a final declaration at ASEM, which commits the 49 leaders gathered to pursuing more effective global economic governance.

In her final hours in the Belgian capital, Ms Gillard held bilateral meetings with the prime ministers of Vietnam and Greece.

Given that there are up to 600,000 Greek nationals living in Australia, the prime minister thought it appropriate to invite prime minister George Papandreou to visit.

"[There's a] very strong Greek community in Melbourne and in Australia that I'm sure would welcome a visit," she said.

"I think he would get a very, very enthusiastic reception if he was able to visit."

The last Greek prime minister to come to Australia was Kostas Karamanlis in 2007.